Abstract

We introduce a new concept of second-order asymptotic directions of unbounded sets and apply it to establish global optimality conditions of nonlinear functions on unbounded sets, existence conditions for efficient points in a partially ordered space, and to extend Dieudonné's theorem on the closedness of the sum of two closed sets.

Author information

Contact details are reproduced from the original publication and may be historical.

Nicolas Hadjisavvas

Dept. of Product and Systems Design, University of the Aegean, 84100 Hermoupolis - Syros, Greece

nhad@aegean.gr

Dinh The Luc

Laboratoire ANLG EA 2151, University of Avignon, 33 Rue Louis Pasteur, 84000 Avignon, France

Keywords

  • First-order and second-order asymptotic directions; optimality conditions; efficient points

Mathematics Subject Classification

90C30, 90C29, 49J52

Suggested citation

N. Hadjisavvas, D. T. Luc. “Second-Order Asymptotic Directions of Unbounded Sets with Application to Optimization.” Journal of Convex Analysis 18 (2011), No. 1, 181–202. https://doi.org/10.68381/jca18010

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.